128 SUMMARY OF CURRENT RESEARCHES RELATING TO 



object which cannot be clearly distinguished by a normal eyo with a 

 sharp immersion amplification of 800.' 



To many microscopists the physical deductions will perhaps bo less 

 accessible than the experiments wbich show that the lines of a microscopic 

 grating are doubled when a portion of the diffracted rays aro prevented 

 from reaching the eye ; that by screening off another part lines can be seen 

 running in a direction different to those of the lines of the grating, &c. 



Even the microscopist who has no desire to work at the theory of 

 theso phenomena must at least be made anxious by them, and his anxiety 

 is the more justified by the fact that there is no criterion by which we 

 can know whether some of the rays have been lost to the retina or not. 



It is this feeling of anxiety with which I am concerned. How many 

 pages have been written upon the structure and the linear markings of 

 PJeurosigma angulatum I We now know that various authors have seen 

 the markings differently, and we know why this is so, and that we may 

 perhaps learn the true structure in some other way, but never by simple 

 microscopic observation as has been attempted. Are we not upon similar 

 ground in the case of the muscle-fibres ? In any case it seems to me 

 that we must tread it with caution. 



Now it is this caution and this feeling of anxiety which I miss in 

 the later investigations on muscle-fibres; although our knowledge of 

 the relation between the diffraction phenomena and the microscopic 

 image is old enough, I do not remember to have ever found in the 

 literature of the subject a clear and definite expression which would 

 indicate any fear of falling into the error which I have pointed out.f 

 Yet facts so glaring as those which I have adduced, and such authors 

 as Helmholtz and Abbe, cannot be overlooked. 



There is a special group of diffraction phenomena to which I will 

 draw attention. The rays which, traverse the object naturally interfere 

 in the wide space between the retina, the 

 object, and (according to the usual optical 

 mode of expression) beyond the latter. 



Let a b (fig. 32) be a plane wave-surface, 

 c d & small opaque particle. In e will meet 

 rays without difference of phase, which have 

 passed c and d and have been diffracted at 

 those points. If then the Microscope is focused 

 upon e a bright spot is seen. As the ob- 

 jective is moved towards c d, i. e. as it is ad- 

 justed for successive points in the line ef 

 which lie between e and c d, the conditions are 

 the same for all these points until the rays 

 d e and c e have so great an inclination, that 

 with the particular aperture in use they no 

 longer contribute to the formation of the 

 image. If the Microscope-tube is depressed until it is adjusted for a 

 point below c d, the bright spot returns and is now due to the rays 

 r/and q /which have no difference of phase. With regard to points 

 lying on either side of the median line ef the case is different. If m is 

 a point at which the diffracted rays c m and d m meet, with a difference 

 of path equal to a half wave-length c h, they destroy one another; e will 



* See infra as to the fear of similar dangers entertained by Heppner and 

 Donitz. 



